000084320 001__ 84320 000084320 005__ 20200909105806.0 000084320 0247_ $$2doi$$a10.1007/s10801-018-0854-y 000084320 0248_ $$2sideral$$a109558 000084320 037__ $$aART-2019-109558 000084320 041__ $$aeng 000084320 100__ $$aAramayona, J. 000084320 245__ $$aTrees, homology, and automorphism groups of right-angled Artin groups 000084320 260__ $$c2019 000084320 5060_ $$aAccess copy available to the general public$$fUnrestricted 000084320 5203_ $$aWe study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree. 000084320 536__ $$9info:eu-repo/grantAgreement/ES/DGA/European Regional Development Funds$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67781 000084320 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000084320 590__ $$a0.805$$b2019 000084320 591__ $$aMATHEMATICS$$b159 / 324 = 0.491$$c2019$$dQ2$$eT2 000084320 592__ $$a0.763$$b2019 000084320 593__ $$aDiscrete Mathematics and Combinatorics$$c2019$$dQ2 000084320 593__ $$aAlgebra and Number Theory$$c2019$$dQ2 000084320 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000084320 700__ $$aFernández, J.L. 000084320 700__ $$aFernández, P. 000084320 700__ $$0(orcid)0000-0001-9147-1745$$aMartínez-Pérez, C.$$uUniversidad de Zaragoza 000084320 7102_ $$12006$$2005$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Algebra 000084320 773__ $$g50, 3 (2019), 293-315$$pJ. algebr. comb.$$tJOURNAL OF ALGEBRAIC COMBINATORICS$$x0925-9899 000084320 8564_ $$s624721$$uhttps://zaguan.unizar.es/record/84320/files/texto_completo.pdf$$yPostprint 000084320 8564_ $$s6781$$uhttps://zaguan.unizar.es/record/84320/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000084320 85641 $$uhttps://link.springer.com/article/10.1007%2Fs10801-018-0854-y (online 2018)$$zTexto completo de la revista 000084320 909CO $$ooai:zaguan.unizar.es:84320$$particulos$$pdriver 000084320 951__ $$a2020-09-09-10:49:51 000084320 980__ $$aARTICLE